22. (12 points) The evil Lord Bolton invests $150,000 in the Totally Secret Nati

Question

22. (12 points) The evil Lord Bolton invests $150,000 in the Totally Secret National Bank of Panama, in an account that pays 7% interest, compounded continuously. The balance in his account, t years after he opens it, will be P) 1500007t How many years after Lord Bolton opens the account will it take for the account balance to reach $270,000 Show all your work, round off your final numerical answer to the nearest 01, if necessary and give your final answer in the form of a complete sentence, using the correct units

Explanation / Answer

P(t) = 150000e^.07t

plugging P(t) = 270,000

270000 = 150000e^.07t

270000 / 150000 = e^.07t

ln ( 27/15 ) = .07t

t = 8.40

so, it takes 8.40 years to reach $ 270,000

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